For what positive value of $t$ is $|6+ti| = 10$?
Since $|6+ti| = \sqrt{6^2 + t^2} = \sqrt{t^2+36}$, the equation $|6+ti| = 10$ tells us that $\sqrt{t^2 + 36} = 10$.  Squaring both sides gives $t^2 + 36= 100$, so $t^2= 64$.  Since we want the positive value of $t$, we have $t = \boxed{8}$.